Recently evidence has come forth which suggests that empirical probability distributions of returns on securities conform better to stable Paretian distributions with infinite variances than to the normal distribution. Using a generalized form of a technique proposed by Sharpe [17] in a recent issue of this journal, this article develops a portfolio analysis model for a stable Paretian market. The article also shows the range of conditions under which diversification is a meaningful economic activity, even though probability distributions of returns on individual securities have infinite variances.